Design Concepts for Hybrid Superconducting-Mechanical Cat Qubits (Part 1)

Dissipatively stabilized cat qubits are bosonic qubits that exhibit an exponential noise bias with photon number, substantially reducing the overhead required for quantum error correction. Here, we present the first of two candidate design concepts for realizing cat qubits based on mechanical storage resonators, where a silicon phononic crystal is coupled to a superconducting nonlinear buffer circuit via an intermediate piezoacoustic cavity. Our design is optimized through consideration of the tradeoff in noise properties of acoustic, piezoelectric, and superconducting materials, careful Hamiltonian engineering, and development of a novel readout scheme which uses the existing buffer circuit hardware to perform cat-transmon gates. Our analysis shows that mechanical-superconducting cat qubits can significantly extend the achievable bit and phase flip times over state-of-the-art all-electrical versions, with natively smaller chip footprints, providing a compelling hybrid hardware platform for achieving scalable, fault-tolerant quantum circuits.